The minorizer, which is concave in transmit covariance matrices, still has the same gradient of the original WSR and hence the KKT conditions are not affected. Now reparameterizing the transmit covariance matrices in terms of beamformer with the optimal power matrices and adding the power constraints to the minorizer, we get the Lagrangian (REF ). By updating all the beamformers and combiners as a dominant generalized eigenvector, leads to an increase in the WSR [1]} at each iteration, thus assuring convergence.
